Neural Combinatorial Optimization for Time Dependent Traveling Salesman Problem

Ruixiao Yang, Chuchu Fan

Keywords: Time Dependent Routing, Neural Combinatorial Optimization, Traveling Salesman Problem, Deep Reinforcement Learning

TL;DR: We propose a state-of-the-art neural-based method for solving Time Dependent Traveling Salesman Problem and identify the limitation of existing evaluation method..

Abstract:

The Time-Dependent Traveling Salesman Problem (TDTSP) extends classical TSP with dynamic edge weights that vary with departure time, reflecting real-world scenarios like transportation networks, where travel times fluctuate due to congestion patterns. TDTSP violates symmetry, triangle inequality, and cyclic invariance properties of classical TSP, creating unique computational challenges.
In this paper, we propose a neural model that extends MatNet from static asymmetric TSP to time-dependent settings through an adjacency tensor that captures temporal variations, followed by a time-aware decoder. Our architecture addresses the unique challenge where asymmetry and triangle inequality violations change dynamically with time.
Beyond architectural innovations, our research reveals a critical evaluation insight: many practical TDTSP instances maintain the same optimal solution regardless of time-dependent edge weights. This exposes a fundamental limitation in current evaluation practices for TDTSP that rely solely on average travel time metrics across all instances. Such metrics fail to effectively distinguish between methods that genuinely capture temporal dynamics and those that merely perform well on static routing problems.
Instead, we present extensive experiments on real-world datasets, evaluating our approach on both entire datasets and specifically filtered instances where temporal dependencies alter the optimal solution. Results show that our method achieves state-of-the-art average optimality gap on full instances and significant travel time reduction on instances for which time-aware routing saves time. These results demonstrate state-of-the-art ability to identify and exploit temporal dependencies while establishing new standards for evaluating routing problems with temporal dependencies.

Primary Area: Optimization (e.g., convex and non-convex, stochastic, robust)

Submission Number: 13424